Abstract: With the tide of globalization, biological invasions and pathogen transmission, which in turn can affect ecosystem or threaten public health, become focal spots in literature. In mathematical biology, there are many reaction-diffusion models arising from various applications such as animal dispersal, geographic spread of epidemics. To model/illustrate these problems/phenomena and investigate/evaluate the corresponding control strategy, it has been proved that the corresponding propagation modes are very important and useful. This minisymposium focus on the recent advances of propagation phenomena of different reaction-diffusion models in biology. In particular, the traveling wave solutions, asymptotic spreading, entire solutions, generalized transmission and threshold dynamics with their applications of reaction-diffusion models will be discussed.

MS-Fr-D-03-113:30--14:00Spreading fronts of invasive species and diseaseLin, Zhigui (Yangzhou Uinversity)Abstract: This talk deals with a diffusive logistic model with a free boundary. We aim to use the dynamics of such a problem to describe the spreading of a new or invasive species. We prove a spreading-vanishing dichotomy for this model . Moreover, we show that when spreading occurs, for large time, the expanding front moves at a constant speed. We also consider an SIS epidemic model with free boundary.

MS-Fr-D-03-214:00--14:30Traveling Wave Solutions of a Diffusion Equation with State-Dependent DelayLin, Guo (Lanzhou Univ.)Abstract: The equation with state-dependent delay does not satisfy the standard comparison principle. We construct a proper wave profile set such that the comparison principle is applicable. By fixed point theorem and the theory of asymptotic spreading, we present the existence and nonexistence of traveling wave solutions.

MS-Fr-D-03-314:30--15:00A Reaction-Diffusion SIS Epidemic Model in an Almost Periodic Environment
Wang, Bin-Guo (School of Mathematics & Statistics, Lanzhou Univ.)Abstract: In this talk, a susceptible-infected-susceptible (SIS) almost periodic reaction-diffusion epidemic model is introduced by means of establishing the theories and properties of the basic reproduction ratio $R_{0}$. Particularly, the asymptotic behaviors of $R_{0}$ with respect to the diffusion rate $D_{I}$ of the infected individuals are obtained. Furthermore, the uniform persistence, extinction and global attractivity are presented in terms of $R_{0}$. Our results indicate that the interaction of spatial heterogeneity and temporal almost periodicity tends to enhance the persistence of the disease. This talk is based on a joint work with Wan-Tong Li and Zhi-Cheng Wang.

MS-Fr-D-03-415:00--15:30Threshold dynamics of a time periodic reaction-diffusion epidemic model with latent periodWang, Zhi-Cheng (Lanzhou Univ.)Abstract: In this talk we first propose a time-periodic reaction-diffusion
epidemic model which incorporates simple demographic structure
and the latent period of infectious disease. Then we introduce
the basic reproduction number R0 for this model
and prove that the sign of R0-1 determines the
local stability of the disease-free periodic solution.
By using the comparison arguments and persistence theory, we further show
that the disease-free periodic solution is globally attractive if
R0-1, while there is an